The only way to make path animation is to bake it with a standard Blender action baker. The menu is under Object->Animation->Bake Action. And then use fresh baked animation without any constraints attached.

But what about animation of visibility? In my case I could make an illusion of movement by switching objects on/off.In one project, I used location animation and moved it far far away to make it dissapear but is there another way?

But what about animation of visibility? In my case I could make an illusion of movement by switching objects on/off.In one project, I used location animation and moved it far far away to make it dissapear but is there another way?

By coincidence, we are now implementing this feature in the NLA Script.